A New Lorentz Violating Model with Particle’s "Maximum Energy"

In Lorentz violating models, the rainbow model or theories of Quantum Gravity are usually discussed, and a common feature of these models is that they assume the particle’s energy have a limited value rather than be infinite derived from the Lorentz model. The introduction of "maximum energy" is considered to be necessary in the combination of Quantum theory and Gravity. However, this paper shows that if we just follow the next three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, then we can totally construct a general coordinate transformation to meet the symmetry of inertial systems, and with a special assumption on the speed of light, we can also construct a non-Lorentz transformation between inertial systems to make the particle’s energy have a limited value. Similar to the usual Lorentz violating models, the non-Lorentz transformation in this paper lead to a new modified disperse relation. We applied the obtained disperse relation to analyze the photon’s arrival time lag effect and found that the "maximum energy" derived in our model is somewhat related to the "maximum energy" assumed in the rainbow model.